Lie angle affects it.  Too upright and you have to choke down to hit it cleanly. Too flat and you have to flex the knees a bit more for the club to lie properly - one key indicator of too flat of a club is you get a considerable amount more distance with a pulled shot vs straight.   When your clubs are more than 1* off from where your proper lie angle is, it is very difficult to hit the ball properly (personal experience is 2* flatter than ideal causes a screaming low hook because you swing flat to compensate).  WIth a proper stance, too flat causes the ball to go right (would be more like a push-slice); with too upright it goes left and the club feels like it turns over at impact (you get more of a pull hook).  

The toe of the iron should point up a slight bit at address (club should lie in the center of the sole).  IF the lie angle is too flat the club feels too short and if too upright it feels too long.

I would bring the irons about 1/2* more upright.  1* max (Take the irons to a fitter and hit them off the lie board to see where the scuff marks are at on the lie tape). 

Also, a fade is caused by an  outside to in swing path (The clubface points at the target but it is open with respect to the swing path).  To get a draw you need an inside-out swing path.

Lie angle will impact ball flight direction, and if your lie angles are too flat, fades, and missing to the right could result. You best option would be to get a fitting for iron lie angles, and compare to where they are now, and adjust from there if required.

I just got fitted for new AP2s at the beginning of the year..i got fitted 2* flat. The adjustment tamed my draw significantly. At upright, my shots with a 6i consistently had a 15-20 yard draw on it. At 2* flat, the draw on the ball was 5 yards or less.

So in my case, and I'm sure in many other cases, the lie angle does make a significant difference in your shot shape.